1. Morfologi citra

2. Operasi Morfologi?
Merubah bentuk.
Morphing

3. Dasar Operasi Himpunan
Konsep himpunan dalam morfologi citra biner
Setiap himpunan menyatakan satu objek. Setiap pixel (x,y) memiliki status : anggota himpunan atau bukan anggota himpuan.

4. Operasi Translasi dan Pencerminan ( Reflection)B A
z = (z1,z2)
(A)z

5. *For binary images only
Logical Operations*
*For binary images only
(Images from Rafael C. Gonzalez and Richard E.
Wood, Digital Image Processing, 2nd Edition.

6. Dilation Operations
= Himpunan kosong
Dilatasi berarti “merentang”
A = Objek yang akan direntang
B = Struktur element

7. Dilation Operations (cont.)
Reflection
Structuring
Element (B)
Original image (A)
Intersect pixel
Center pixel

8. Dilation Operations (cont.)
Result of Dilation
Boundary of the “center pixels”
where intersects A

9. Example: Application of Dilation
“Repair” broken characters
(Images from Rafael C. Gonzalez and Richard E.
Wood, Digital Image Processing, 2nd Edition.

10. Erosion berarti “ramping”
Operasi erosi
Erosion berarti “ramping”
A = Object untuk dirampingkan
B = Struktur elemen

11. Operasi Erosi (cont.) Struktur elemen (B) Citra Asal (A)
Intersect pixel
Center pixel

12. Erosion Operations (cont.)
Result of Erosion
Boundary of the “center pixels”
where B is inside A

13. Example: Application of Dilation and Erosion
Menghilangkan objek kecil seperti noise
(Images from Rafael C. Gonzalez and Richard E.
Wood, Digital Image Processing, 2nd Edition.

14. Keterkaitan Dilatasi dan Erosi
dimana c = komplemen
Bukti:

15. Operasi Opening
atau
= Gabungan dari semua bagian dari A yang benar-benar berisi B
Opening menghilangkan detail dan sudut
(Images from Rafael C. Gonzalez and Richard E.
Wood, Digital Image Processing, 2nd Edition.

16. Contoh Opening

17. Operasi Closing
Closing mengisi celah sempit dan lekukan

18. Contoh Closing

19. Hubungan antara Opening dan Closing
Sifat Opening
Sifat Closing

20. Contoh: Aplikasi dari operasi morfologi
Perbaikan Finger print
(Images from Rafael C.
Gonzalez and Richard E.
Wood, Digital Image
Processing, 2nd Edition.

21. Hit-or-Miss Transformation*
dimana X = bentuk yang dideteksi
W = window yang berisi X
(Images from Rafael C. Gonzalez and Richard E.
Wood, Digital Image Processing, 2nd Edition.

22. Hit-or-Miss Transformation (cont.)*
(Images from Rafael C.
Gonzalez and Richard E.
Wood, Digital Image
Processing, 2nd Edition.

23. Boundary Extraction Original Boundary image (Images from Rafael C.
Gonzalez and Richard E.
Wood, Digital Image
Processing, 2nd Edition.

24. Hit-or-Miss Operator Definition * Structuring element example _ _ X B=
(X B1)(Xc B2)
Hit
Miss
Structuring element example
origin
1 -1 x x x
mask B1
mask B2
mask B
MATLAB
(MATLAB function: bwhitmiss)

25. Example 1 _ _ X
X B1
Xc B2 Xc
origin
X B *
mask B1
mask B2

26. origin * Interseksi Contoh -1 -1 -1 1 -1 1 1 -1 mask B1 mask B2 mask B
1 -1
mask B1
mask B2
mask B
MATLAB _ _ X
X B1
Xc B2 Xc
X B *
Interseksi

27. Region Filling dimana X0 = p Citra asal Hasil dari region filling
(Images from Rafael C. Gonzalez and Richard E.
Wood, Digital Image Processing, 2nd Edition.

28. Extraction of Connected Components
dimana X0 = p
(Images from Rafael C. Gonzalez and Richard E.
Wood, Digital Image Processing, 2nd Edition.

29. Example: Extraction of Connected Components
X-ray image
of bones
Thresholded
image
Connected
components
(Images from Rafael C.
Gonzalez and Richard E.
Wood, Digital Image
Processing, 2nd Edition.

30. Bentuk Struktur Elemen
x = don’t care
(Images from Rafael C. Gonzalez and Richard E.
Wood, Digital Image Processing, 2nd Edition.

31. SELESAI

32. Gray-Scale Dilation 1-D Case 2-D Case
(Images from Rafael C. Gonzalez and Richard E.
Wood, Digital Image Processing, 2nd Edition.

33. Gray-Scale Dilation (cont.)
Original image
Reflection
of B
Subimage +
Max
Moving
window
Structuring
element B
Note: B can be any shape and
subimage must have
the same shape as
reflection of B.
Output image

34. Gray-Scale Erosion 1-D Case 2-D Case
(Images from Rafael C. Gonzalez and Richard E.
Wood, Digital Image Processing, 2nd Edition.

35. Gray-Scale Erosion (cont.)
Original image
Subimage B -
Min
Moving
window
Structuring
element B
Note: B can be any shape and
subimage must have
the same shape as B.
Output image

36. Example: Gray-Scale Dilation and Erosion
Original image
After dilation
Darker
Brighter
After erosion
(Images from Rafael C. Gonzalez and Richard E.
Wood, Digital Image Processing, 2nd Edition.

37. Gray-Scale Opening Opening cuts peaks
(Images from Rafael C. Gonzalez and Richard E.
Wood, Digital Image Processing, 2nd Edition.

38. Gray-Scale Closing Closing fills valleys
(Images from Rafael C. Gonzalez and Richard E.
Wood, Digital Image Processing, 2nd Edition.

39. Example: Gray-Scale Opening and Closing
Original image
After opening
After closing
Reduce dark
objects
Reduce white
objects
(Images from Rafael C. Gonzalez and Richard E.
Wood, Digital Image Processing, 2nd Edition.

40. Gray-scale Morphological Smoothing
Smoothing: Perform opening followed by closing
Original image
After smoothing
(Images from Rafael C. Gonzalez and Richard E.
Wood, Digital Image Processing, 2nd Edition.

41. Morphological Gradient
Original image
(Images from Rafael C. Gonzalez and Richard E.
Wood, Digital Image Processing, 2nd Edition.

42. Top-Hat Transformation
Results of top-hat transform
Original image
(Images from Rafael C. Gonzalez and Richard E.
Wood, Digital Image Processing, 2nd Edition.

43. Example: Texture Segmentation Application
Small
blob
Original image
Segmented result
Large blob
Algorithm:
1. Perform closing on the image by using successively larger
structuring elements until small blobs are vanished.
2. Perform opening to join large blobs together
3. Perform intensity thresholding
(Images from Rafael C. Gonzalez and Richard E.
Wood, Digital Image Processing, 2nd Edition.

44. Example: Granulometry
Objective: to count the number of particles of each size
Method:
1. Perform opening using structuring elements of increasing size
2. Compute the difference between the original image and the result
after each opening operation
3. The differenced image obtained in Step 2 are normalized and used
to construct the size-distribution graph.
Size distribution
graph
Original image
(Images from Rafael C. Gonzalez and Richard E.
Wood, Digital Image Processing, 2nd Edition.

45. Morphological Watershads
(Images from Rafael C. Gonzalez and Richard E.
Wood, Digital Image Processing, 2nd Edition.

46. Morphological Watershads
(Images from Rafael C. Gonzalez and Richard E.
Wood, Digital Image Processing, 2nd Edition.

47. Morphological Watershads
(Images from Rafael C. Gonzalez and Richard E.
Wood, Digital Image Processing, 2nd Edition.

48. Gradient Image
Original
image
Surface of
at edges look
like mountain ridges.

49. Morphological Watershads
(Images from Rafael C. Gonzalez and Richard E.
Wood, Digital Image Processing, 2nd Edition.

50. Morphological Watershads
(Images from Rafael C. Gonzalez and Richard E.
Wood, Digital Image Processing, 2nd Edition.

51. Morphological Watershads
(Images from Rafael C. Gonzalez and Richard E.
Wood, Digital Image Processing, 2nd Edition.

52. Convex Hull (Images from Rafael C. Gonzalez and Richard E.
Wood, Digital Image Processing, 2nd Edition.